• Korean Journal of Computational Design and Engineering
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• v.11 no.1
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• pp.1-10
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• 2006

This paper addresses B-spline curve approximation of a set of ordered points to a specified toterance. The important issue in this problem is to reduce the number of control points while keeping the desired accuracy in the resulting B-spline curve. In this paper we propose a new method for error-bounded B-spline curve approximation based on adaptive selection of dominant points. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within the tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each step by averaging the parameters of the dominant points. The resulting curve is a piecewise B-spline curve of order (degree+1) p with $C^{(p-2)}$ continuity at each knot. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with previous methods for error-bounded B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity. Some experimental results demonstrate its usefulness and quality.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.1-11
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• 1994

In computer graphics since objects atre constructed by lines and curves, the high-speed curve generator is indispensible for computer aided design and simulatation. Since the functions of graphic generation can be represented as a series of matrix operations, in this paper, two kind of the high-speed Bezier curve generator that uses matrix equation and a recursive relation for Bezier polynomials are designed. And B-spline curve generator is designed using interdependence of B-spline blending functions. As the result of the comparison of designed curve generator and reference [5], [6] in the operation time and number of operators, the curve generator with 1-dimensional systolic array processor for matrix vector operation that uses matrix equation for Bezier curve is more effective.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.9 no.1
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• pp.85-102
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• 1999

In this paper, we propose an EC-SRP(Elliptic Curve - Secure Remote Password) protocol that uses ECDLP(Elliptic Curve Discrete Logarithm Problem) instead SRP protocols’s DLP. Since EC-SRP uses ECDLP, it inherits the high performance and security those are the properties of elliptic curve. And we reduced the number of elliptic curve scalar multiplication to improve EC-SRP protocol’s performance. Also we have proved BC-SRP protocol is a secure AKC(Authenticated Key Agreement with Key Confirmation) protocol in a random oracle model.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.474-479
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• 2003

This paper addresses the problem of B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. A traditional lofting approach creates a set of B-spline curves via B-spline curve interpolation to each contour, makes them compatible via degree elevation and knot insertion, and performs B-spline surface lofting to get a B-spline surface interpolating them. The approach tends to result in an astonishing number of control points in the resulting B-spline surface. This situation arises mainly from the inevitable process of progressively merging different knot vectors to make the B-spline curves compatible. This paper presents a new approach for avoiding this troublesome situation. The approach includes a novel process of getting a set of compatible B-spline curves from the given contours. The process is based on the universal parameterization [1,2] allowing the knots to be selected freely but leading to a more stable linear system for B-spline curve interpolation. Since the number of control points in each compatible B-spline curve is equal to the highest number of contour points, the proposed approach can realize efficient data reduction and provide a compact representation of a B-spline surface while keeping the desired surface shape. Some experimental results demonstrate its usefulness and quality.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2000.04a
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• pp.475-478
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• 2000

Recently encryption algorithms based on difficulties of factorization have been used with popularization. Prime number factorizations are progressed rapidly. In this paper, characteristics of elliptic curve are analyzed and generation of elliptic curves suitable for prime number factorization is discussed.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.493-498
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• 1999

To extract hydrologic information more easily , the pre-processor for hydrologic model using Geographic Information System was developed . This model was applied to the Balan-reservoir watershed which is located at the southwest of Suwon. For estimation SCS curve number, landuse map and hydrologic soil group map were collected from digital map and reconnaissance soil map respectively. The estimated curve number from the GIS technique was 73.

• Korean Journal of Environment and Ecology
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• v.9 no.2
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• pp.197-201
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• 1996

A mixed forest community of Abies holophylla and broad-leaved trees in Odaesan National Park was studied to determine the adequate number of plots of shrub stratum for investigating forest community structure. Thirty 5m*5m plots were set up in the shrub stratum, and species-area curve and performance curve were made out. The minimum number of plots where a given percentage increase in number of plots produce in number of plots produced less than the same percentage increase in number of species was six. The minimum number of plots where a given percentage increase in number of plots produced less than the half of the percentage increase in number of plots was eleven. The minimum number of plots where the dominant species was distinguished from the subdominant species was five. The minimum numver of plots where the first subdominant species was distinguished from other subdominant species was ten. The diffrence of species diversity(H') between five or more plots and total thirty plots was less than 0.05. Similarity index was more than 70% between five or more plots and total thirty plots, and more than 80% between ten or more plots and total thirty plots. The conclusion is that the adequate number of 5m*5m plots for the shrub stratum was about 5 in general case and about 10 in case of requiring more accuracy.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.113-120
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• 1998

Calculation of intersection points by two curves is fundamental to computer aided geometric design. Bezier clipping is one of the well-known curve intersection algorithms. However, this algorithm is only applicable to Bezier curve representation. Therefore, the NURBS curves that can represent free from curves and conics must be decomposed into constituent Bezier curves to find the intersections using Bezier clipping. And the respective pairs of decomposed Bezier curves are considered to find the intersection points so that the computational overhead increases very sharply. In this study, extended Bezier clipping which uses the linear precision of B-spline curve and Grevill's abscissa can find the intersection points of two NURBS curves without initial decomposition. Especially the extended algorithm is more efficient than Bezier clipping when the number of intersection points is small and the curves are composed of many Bezier curve segments.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.168-174
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• 2000

A biarc is a curve connecting two circular arcs with the constraints of tangent continuity so that it can represent the free form currie approximately connecting several biarcs with the tangent continuity. Since a biarc consists of circular arcs, the offset curve of the curve represented by biarcs can be easily obtained. Besides. if the tool path is represented by biarcs, the efficiency of machining is improved and the amount of data is decreased. When approximating a curve with biarcs, the location of the point where two circular arcs meet each other plays an important part in determining the shape of a biarc. In this thesis, the optimum point where two circular arcs meet is calculated using the tangent information of the curve to approximate so that it takes less calculation time to approximate due to the decrease of the number of iterations.

• The Journal of Information Technology
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• v.5 no.1
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• pp.99-111
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• 2002

Due to non-linear characteristics of color spaces, color corrections using linear conversions for real image near color reappearance causes color distortions. In order to overcome this problem, the Bezier Curve, constructed with a set of arbitrary plane in the linear theory, has been used. However, the Bezier Curve increases in proportion to the number of data points, resulting in higher computational complexities. This paper attempts to use a Triplicated Piecewise Bezier Cubic-Curve (TPBC-Curve) of which the degree is cubic on the whole interval while keeping the characteristics of Bezier Curves. By Comparing the TPBC-Curve with Bezier Curve of 20 degree, the paper not only reduces the distortion during color correction but also lessens the relative increase of workload that is caused by the color correction in a small zone.